How to fix linux not sending mail problem: Sendmail stat=Deferred: Connection refused by [127.0.0.1]

I recently experienced a problem where my server was not sending mail from the PHP mail() function or the command line "mail" function. After looking through /var/log/maillog, I was able to see that the local 127.0.0.1 mail server was refusing the connection. Some Google searching landed me at the following thread, where the third post did the trick:

http://www.howtoforge.com/forums/showthread.php?t=16246

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